Final answer:
To solve the system of equations, use the method of elimination to eliminate one variable by adding the two equations together. Solve for the remaining variable and substitute its value back into one of the original equations to find the other variable.
Step-by-step explanation:
The given system of equations is:
x - 2y = 4
3x + 2y = 4
To solve this system, you can use the method of elimination. By adding the two equations together, we can eliminate the variable y:
(x - 2y) + (3x + 2y) = 4 + 4
Simplifying:
4x = 8
Dividing both sides by 4:
x = 2
Substituting the value of x into one of the original equations:
3(2) + 2y = 4
Simplifying:
6 + 2y = 4
Subtracting 6 from both sides:
2y = -2
Dividing both sides by 2:
y = -1
Therefore, the solution to the system of equations is x = 2 and y = -1.